CAPE CANAVERAL — Blame it on growing pains or whatever you wish, but the 7,500 residents of this 2-square-mile community -- more than half of them registered voters -- seem to have a knack for controversy.

Just as a monthslong battle over fire protection seems to be ending, city officials are talking about ways to save the Cape Canaveral library, which is about to fall victim to a countywide reorganization.

A 0.5 mill increase would cost the owner of a $50,000 home with a $25,000 homestead exemption about $12.50 a year.

The city has dropped its financial support of the independent Cape Canaveral Volunteer Fire Department Inc. It organized its own eight-member paid fire department in March.

The volunteers presented a petition on Aug. 19 calling for an ordinance to abolish the paid department. It also would lock the city into an exclusive contract with the 27-member volunteer force that has served residents since Cape Canaveral was founded 23 years ago.

Council also has voted to cancel its three-way fire protection contract with the volunteers and the independent taxing district of Port Canaveral.

The agreement expires in January.

Council on Tuesday ordered newly appointed City Attorney Jim Theriac and Councilman Jerry Fischetti to meet with petition committee attorney Harold Bistline ''to reach some kind of accord,'' said City Manager Fred Nutt.

At a workshop next Thursday, city council members will discuss a possible tax increase of up to a half mill to build a new 8,000-square-foot library next to city hall if the county goes ahead with plans to close the Cape Canaveral library.

A mill is $1 in taxes for every $1,000 of non-exempt assessed property value.

A .5 mill increase would cost the owner of a $50,000 home with a $25,000 homestead exemption about $12.50 a year.

If approved, the issue would be placed on the November ballot. The new building would replace the library on Caroline Street when its lease expires in three years.

A recent 60 percent increase in sewer bills has angered some Cape Canaveral residents. Nutt said taxpayers were surprised at the increase even though the issue was discussed several times during council meetings.

He said there has not been an increase since 1981. Additional funds were needed to meet revenue requirements for a bond issue when the waste water treatment plant added a second work shift in 1982-83.

Other problems council faces are:

-- The city's strained relationship with bordering Port Canaveral. Fischetti says Port Director Charles Rowland is trying to tell council members how to run the city by suggesting the council sign a reciprocating fire protection agreement with the port when the three-way contract expires.

Rowland, who in the past five years has helped bring the port's annual income to more than twice that of Cape Canaveral's $1.7 million general funds revenue, says he thinks ''there's some jealousy'' because the port is growing so fast.

''I think the port has tried to get along with the city,'' he said. ''Some of the people in city politics don't understand the purpose of the port.''

Rowland and Fischetti agree the two taxing districts have gone their separate ways and that they will have less to do with each other as time goes on.

One problem may have to be resolved before the two sides resolve their differences. Fischetti says he is waiting for cooler weather to see if the port has corrected a scallop odor problem that began last year.

Rowland says the issue is dead and buried. The port has been using smelly scallop plant waste as land fill since early summer.

Fischetti said the odor is less evident during the summer, and that he will give the port's solution a sniff test this fall.

-- The lack of a shopping center or a motel on State Road A1A, the city's main artery. A 90,000-square-foot shopping center is on the drawing board, but the proposed site next to the Rockwell building required a zoning change.

A proposed motel ''somewhere along A1A leading to S.R. 528'' also would require a zoning change, Fischetti said.

Such changes seem to draw the attention of at least three Cape Canaveral residents: former Mayor Ann Thurm; former council member Joan Calvert; and Helen Filkins, a past president of the Cape Canaveral Civic Association.

Thurm is a member of the board of adjustments and her husband, Dick, also a former mayor, is on the zoning board.

But it is Mrs. Thurm and company who declare all-out war when attempts are made to change the city's 15-units-per-acre zoning ordinance.

Such was the case recently when developers were temporarily successful in getting a beachfront site rezoned for construction of a Radisson Hotel.

''The City Council tried to sneak in a hotel in an area on the beach but we forced them to change their minds,'' Filkins said of the subsequent battle over possible violations of the state Comprehensive Land Use Act. ''We will fight everything that council tries to pull if it has to do with growth.''